A digital phase-locked loop is introduced, which is specifically developed for frequency detection. The digital oscillator is realized with a coupled-form digital filter structure and a Hilbert transform is used for phase detection. The quadrature of the input signal is formed from two samples of the actual input signal. In this paper explicit formulas are derived for the noise variance in the frequency detector and for the acquisition time. The results of the digital phase-locked loop are compared with those of an adaptive digital filter with a resonator in the feedback loop